4420 Words18 Pages

Linear Regression Models

1

SPSS for Windows® Intermediate & Advanced Applied Statistics Zayed University Office of Research SPSS for Windows® Workshop Series Presented by Dr. Maher Khelifa Associate Professor Department of Humanities and Social Sciences College of Arts and Sciences

© Dr. Maher Khelifa

2

Bi-variate Linear Regression

(Simple Linear Regression)

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

3

Many statistical indices summarize information about particular

phenomena under study.

For example, the Pearson (r) summarizes the magnitude of a linear

relationship between pairs of variables.

However, one major scientific research objective is to “explain”,

“predict”, or*…show more content…*

The parameters β0 and β1 are constants describing the functional relationship in the population. The value of β1 identifies the change along the Y scale expected for every unit changed in fixed values of X (represents the slope or degree of steepness). The values of β0 identifies an adjustment constant due to scale differences in measuring X and Y (the intercept or the place on the Y axis through which the straight line passes. It is the value of Y when X = 0). ∑ (Epsilon) represents an error component for each individual. The portion of Y score that cannot be accounted for by its systematic relationship with values of X.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

12

•

The formula Y = β0 + β1X + ε can be thought of as:

Yi = Y’+ εi (where α + β1Xi define the predictable part of any Y score for fixed values of X. Y’ is considered the predicted score).

•

The mathematical equation for the sample general linear model is represented as:

Yi = b0 + b1Xi + ei.

•

In this equation the values of a and b can be thought of as values that maximize the explanatory power or predictive accuracy of X in relation to Y. In maximizing explanatory power or predictive accuracy these values minimize prediction error. If Y represents an individual’s score on the criterion variable and Y’ is the predicted score, then Y-Y’ = error score (e) or the

1

SPSS for Windows® Intermediate & Advanced Applied Statistics Zayed University Office of Research SPSS for Windows® Workshop Series Presented by Dr. Maher Khelifa Associate Professor Department of Humanities and Social Sciences College of Arts and Sciences

© Dr. Maher Khelifa

2

Bi-variate Linear Regression

(Simple Linear Regression)

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

3

Many statistical indices summarize information about particular

phenomena under study.

For example, the Pearson (r) summarizes the magnitude of a linear

relationship between pairs of variables.

However, one major scientific research objective is to “explain”,

“predict”, or

The parameters β0 and β1 are constants describing the functional relationship in the population. The value of β1 identifies the change along the Y scale expected for every unit changed in fixed values of X (represents the slope or degree of steepness). The values of β0 identifies an adjustment constant due to scale differences in measuring X and Y (the intercept or the place on the Y axis through which the straight line passes. It is the value of Y when X = 0). ∑ (Epsilon) represents an error component for each individual. The portion of Y score that cannot be accounted for by its systematic relationship with values of X.

© Dr. Maher Khelifa

Understanding Bivariate Linear Regression

12

•

The formula Y = β0 + β1X + ε can be thought of as:

Yi = Y’+ εi (where α + β1Xi define the predictable part of any Y score for fixed values of X. Y’ is considered the predicted score).

•

The mathematical equation for the sample general linear model is represented as:

Yi = b0 + b1Xi + ei.

•

In this equation the values of a and b can be thought of as values that maximize the explanatory power or predictive accuracy of X in relation to Y. In maximizing explanatory power or predictive accuracy these values minimize prediction error. If Y represents an individual’s score on the criterion variable and Y’ is the predicted score, then Y-Y’ = error score (e) or the

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